Advanced Engineering Mathematics, 7th Edition

9.14 Stokes’ Theorem

INTRODUCTION

Green’s theorem of the preceding section has two vector forms. In this and in Section 9.16 we shall generalize these forms to three dimensions.

Vector Form of Green’s Theorem

If F(x, y) = P(x, y)i + Q(x, y)j is a two-dimensional vector field, then

From (12) and (13) of Section 9.8, Green’s theorem can be written in vector notation as

(1)

that is, the line integral of the tangential component of F is the double ...